Call center queuing system performance prediction method and device, terminal and storage medium
By constructing a quasi-birth-death process and utilizing the RG decomposition method, and comprehensively considering various customer behaviors in the call center queuing system, the problem of inaccurate prediction in existing models is solved, and accurate prediction of system performance and resource optimization are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HEBEI NORMAL UNIVERSITY OF SCIENCE & TECHNOLOGY
- Filing Date
- 2025-12-30
- Publication Date
- 2026-04-21
AI Technical Summary
Existing call center queuing system performance analysis models cannot simultaneously consider the combined effects of multiple behaviors such as customer abandonment, system-initiated disconnection, and customer feedback, leading to inaccurate performance predictions and affecting system resource allocation and operational strategy optimization.
A quasi-birth-death process is constructed, and the RG decomposition method is combined to comprehensively consider the behavior of negative customers, impatient customers, and feedback customers. By obtaining system parameters such as stage distribution parameters, service rate, impatience rate, and feedback probability, performance indicators such as average queue length and average customer dwell time are calculated.
It improves the accuracy of queuing system performance prediction, helps call center managers to allocate resources rationally, improve resource utilization efficiency, and optimize service quality.
Smart Images
Figure CN121907960A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of queuing theory and system performance evaluation technology, and in particular to a method, device, terminal and storage medium for predicting the performance of a call center queuing system. Background Technology
[0002] Existing performance analysis models for queuing systems such as call centers mostly consider only a single customer behavior (e.g., customer abandonment). In actual operation, customer abandonment, system disconnection due to timeouts (negative customers), and customers requiring multiple services (feedback) coexist and interact with each other. Existing models cannot accurately characterize the combined effect of these three behaviors, leading to significant deviations in predictions of key system performance indicators (such as average wait time, system throughput, and customer churn rate) from reality. This renders system capacity planning and operational strategy optimization based on these models ineffective. Summary of the Invention
[0003] This application provides a method, apparatus, terminal, and storage medium for predicting the performance of a call center queuing system, in order to solve the problem of inaccurate prediction results in existing queuing systems.
[0004] Firstly, this application provides a method for predicting the performance of a call center queuing system, including: Obtain the system parameters of the target queuing system, including stage distribution parameters, service rate, impatience rate, negative customer arrival rate, and feedback probability; Based on the system parameters of the target queuing system, a pseudo-birth-death process is constructed; The quasi-birth-death process is decomposed using RG decomposition to calculate the performance indicators of the target queuing system, including the average queue length and the average customer dwell time.
[0005] Secondly, this application provides a call center queuing system performance prediction device, comprising: The parameter acquisition module is used to acquire the system parameters of the target queuing system, including the stage distribution parameters, service rate, impatience rate, negative customer arrival rate, and feedback probability. The process construction module is used to construct a pseudo-birth and death process based on the system parameters of the target queuing system; The performance calculation module is used to perform RG decomposition on the quasi-birth-death process and calculate the performance indicators of the target queuing system, including the average queue length and the average customer stay time.
[0006] Thirdly, this application provides a terminal including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method as described in the first aspect or any possible implementation of the first aspect above.
[0007] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method as described in the first aspect or any possible implementation thereof.
[0008] This application provides a method, apparatus, terminal, and storage medium for predicting the performance of a call center queuing system. The method involves acquiring system parameters of the target queuing system, including staged distribution parameters, service rate, impatience rate, negative customer arrival rate, and feedback probability. Based on these parameters, a quasi-birth-death process is constructed. This process is then subjected to RG decomposition to calculate the performance indicators of the target queuing system, including average queue length and average customer dwell time. The quasi-birth-death process, a powerful mathematical tool capable of accurately describing queuing systems with complex state transitions, is constructed based on the acquired system parameters. By abstracting the actual queuing system into a quasi-birth-death process, the transition patterns between different states can be more accurately characterized, thereby improving the accuracy of performance indicator calculations. Furthermore, accurately predicting performance indicators such as average queue length and customer dwell time helps call center managers understand the system's operational status under different conditions. Simultaneously, based on the predicted customer dwell time, service resources can be rationally allocated to ensure customers receive service within a reasonable timeframe, improving resource utilization efficiency. Attached Figure Description
[0009] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0010] Figure 1 This is a flowchart illustrating the call center queuing system performance prediction method provided in this application embodiment; Figure 2 This is a schematic diagram of the state transition relationship of the first pseudo-birth and death process provided in the embodiments of this application; Figure 3 This is a schematic diagram of the state transition relationship diagram of the second pseudo-birth and death process provided in the embodiments of this application; Figure 4This is a schematic diagram of the structure of the call center queuing system performance prediction device provided in the embodiments of this application; Figure 5 This is a schematic diagram of the terminal provided in the embodiments of this application. Detailed Implementation
[0011] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.
[0012] To make the objectives, technical solutions, and advantages of this application clearer, the following description will be provided in conjunction with the accompanying drawings and specific embodiments.
[0013] Existing methods cannot simultaneously characterize the combined effects of negative customers, impatient customers, and feedback customers, leading to inaccurate performance predictions in real-world queuing systems such as communication networks and call centers. For example, because existing methods fail to fully reflect the operational mechanisms of real systems, when applied to modern, complex call centers or service queuing systems, performance predictions based on these methods (such as "only 20 seats are needed to guarantee service levels") will significantly deviate from the actual performance of the queuing system (which actually requires 25 seats). This deviation can result in misallocation of system resources—either excessive resources leading to waste, or insufficient resources leading to decreased service quality and customer churn.
[0014] A negative customer is a special type of customer who does not request service. Their arrival removes a positive customer who is currently queuing or receiving service in the system. The removal rule can be changed from "remove the customer at the front of the queue" to "remove the customer at the back of the queue" or other random removal rules.
[0015] An impatient customer is one who leaves the system because the waiting time is too long.
[0016] Feedback customers are those who, after their service has been completed, rejoin the queue because the problem was not completely resolved or they are dissatisfied, waiting to be served again.
[0017] To overcome the aforementioned problems, this application provides a call center queuing system performance prediction method that comprehensively models negative customers, impatient customers, and feedback customers, thereby achieving more accurate prediction and more effective optimization of queuing system performance. Its core is to construct a state-dependent quasi-birth-death process that can simultaneously accommodate the three types of customer behavior, and to use the RG decomposition method to efficiently and accurately solve this complex process analytically, obtaining a stationary probability vector for the queuing system. Based on this stationary probability vector, closed-form expressions or efficient numerical algorithms for key performance indicators such as average queue length and average customer dwell time can be derived, thus providing accurate data support for queuing system optimization. Furthermore, to address the computational challenges posed by the theoretically infinite state space, a numerical truncation and iterative algorithm is executed.
[0018] The quasi-birth-death process is a hierarchical Markov process and a core mathematical tool for analyzing complex queuing systems. Its state is described by both "levels" (such as the total number of customers in the system) and "stages" (such as the current stage of the arrival process).
[0019] RG decomposition is a matrix factorization method for solving the steady-state probabilities of Markov processes. By decomposing the complex transition matrix into measures such as R and G, the probabilities of the system in each state can be calculated efficiently.
[0020] Average customer dwell time is the average time a customer spends from entering the system until they eventually leave the system (whether due to service completion, impatience, or removal by a negative customer).
[0021] Stationary probability vector: The probability distribution of a system in each possible state when it reaches a steady state after running for a long time.
[0022] This application's embodiments are the first to integrate three key behaviors—negative customers, impatient customers, and feedback customers—within a unified queuing system framework, making performance predictions more closely resemble real-world application scenarios such as call centers. Furthermore, based on rigorous mathematical derivation and an efficient RG decomposition algorithm, it can provide faster and more accurate steady-state performance indicator predictions than simulations and simplified models, providing a reliable basis for scientific operational decisions (such as agent scheduling and overtime policy settings). Simultaneously, this application's embodiments have good scalability and can be easily adapted to other complex service systems by replacing the arrival process (e.g., using a Markov arrival process), service distribution, or removal rules.
[0023] Figure 1 The implementation flowchart of the call center queuing system performance prediction method provided in the embodiments of this application is described in detail below: In step 101, the system parameters of the target queuing system are obtained. The system parameters include stage distribution parameters, service rate, impatience rate, negative customer arrival rate, and feedback probability.
[0024] The staged distribution is a probability distribution used to describe non-exponential distributions, and it can approximate any non-negative random variable by combining multiple exponential stages. In this invention, it is used to simulate the irregularity of customer arrival times.
[0025] In this embodiment, system parameters of the target queuing system are acquired using sensors or memory. These system parameters may include, but are not limited to, stage-type distribution parameters. Service speed Impatient speed Negative customer arrival rate and feedback probability .
[0026] The system parameters obtained in this application's embodiments cover multiple aspects, including staged distribution parameters, service rate, impatience rate, negative customer arrival rate, and feedback probability. These parameters reflect the operational characteristics of the call center queuing system from different dimensions. For example, service rate reflects the service personnel's ability to handle business, impatience rate reflects changes in customers' psychology and behavior during the waiting process, and negative customer arrival rate and feedback probability consider the impact of special circumstances on the system. Comprehensive consideration of these factors makes the constructed model closer to the actual system, thereby enabling more accurate prediction of system performance indicators, such as average queue length and customer dwell time.
[0027] In step 102, a pseudo-birth and death process is constructed based on the system parameters of the target queuing system.
[0028] In this embodiment of the application, based on the system parameters of the target queuing system obtained in step 101, a horizontally dependent pseudo-birth and death process is constructed in the computing device to describe the dynamics of the target queuing system where positive customers, negative customers, impatient customers and feedback customers coexist.
[0029] This application's embodiments construct a quasi-birth-death process based on acquired system parameters. A quasi-birth-death process is a powerful mathematical tool capable of accurately describing queuing systems with complex state transitions. By abstracting the actual queuing system into a quasi-birth-death process, the transition patterns between different states can be more accurately characterized, thereby improving the accuracy of system performance index calculations.
[0030] In one possible implementation, the pseudo-birth-death process may include a first pseudo-birth-death process determined by the number of customers and the customer arrival process stage; the pseudo-birth-death process is constructed based on the system parameters of the target queuing system, and may include: Based on the number of customers and the stages of the customer arrival process, construct the state transition relationship of a two-dimensional Markov process; The state space is determined based on the state transition relationship of a two-dimensional Markov process. Based on the state space, the first pseudo-birth and death process is obtained.
[0031] Optionally, when the quasi-birth and death process is determined by the number of customers Customer arrival process stage When the first pseudo-birth-death process is determined, the construction process of the first pseudo-birth-death process is as follows: Based on customer number Customer arrival process stage Constructing the state transition relations of a two-dimensional Markov process The corresponding state transition diagram is referenced. Figure 2 As shown in the diagram. Here, Arrival process refers to the phased distribution parameters, Removal process refers to the negative customer arrival rate, Service process refers to the service rate, and Impatience process refers to the impatience rate.
[0032] Then, based on the state transition relationship of the two-dimensional Markov process... , thus obtaining the state space ,Right now .
[0033] The first pseudo-birth-death process of a two-dimensional Markov process is:
[0034]
[0035]
[0036]
[0037]
[0038] in, This is the generator matrix of the first pseudo-birth-death process. For state In the direction of transfer The rate matrix, For state levels, , To change direction, This indicates that the transfer direction is within the same level. This indicates that the transfer direction is upward. This indicates that the transfer direction is downwards; It is the identity matrix. The transition rate matrix is the parameter of the stage distribution. This is the initial probability vector for the stage distribution parameters. For feedback probability, For service speed, For negative customer arrival rate, For impatient speed.
[0039] Among them, the customer arrival process stage in the embodiments of this application It can also be replaced by Markov arrival processes or batch Markov arrival processes to characterize the correlation between arrivals.
[0040] In one possible implementation, the quasi-birth-death process may further include a second quasi-birth-death process determined by the number of customers when the target customer arrives, the number of customers after the target customer arrives, and the customer arrival process stage, wherein the target customer is a customer who arrives at any time in the target queuing system. Based on the system parameters of the target queuing system, a pseudo-birth-death process can be constructed, which may include: Based on the number of customers when the target customer arrives, the number of customers after the target customer arrives, and the stage of the customer arrival process, a Markov process with an absorption state is constructed. Based on the Markov process with an absorbing state, a second pseudo-birth-death process is constructed.
[0041] Optionally, when the quasi-birth-death process is a second quasi-birth-death process determined by the number of customers when the target customer arrives, the number of customers after the target customer arrives, and the stages of the customer arrival process, the construction process of the second quasi-birth-death process is as follows: Assuming there are customers ahead of the target customer One customer, followed by... The stay time of each customer is In this application embodiment, the calculation is performed by constructing a Markov process with an absorbing state.
[0042] make Indicates the target customer at any given time The number of customers arriving at the queuing system Indicates the target customer at any given time Number of customers upon arrival Indicates the target customer at any given time Upon reaching the process stage, it enters an absorption state. The state transition relation of a Markov process is as follows: Accordingly, the state transition diagram can be referenced. Figure 3 As shown.
[0043] Specifically, having an absorption state The second pseudo-birth-death process of the Markov process is:
[0044]
[0045]
[0046]
[0047]
[0048]
[0049]
[0050]
[0051]
[0052]
[0053]
[0054] in, This is the generator matrix of the second pseudo-birth-death process. For absorption state transition block, This is a non-absorption state transition block. The transfer rate block between non-absorption states. hierarchical Towards hierarchy Transfer sub-blocks, For the transition from non-absorbing state to absorbing state The transfer rate block, , , These are sub-blocks that transition from different levels to the absorption state. The rate of downward transfer is due to the combined effects of poor service, impatience, and negative customer behavior. To balance the arrival rate of new customers with the departure rate of various customer types within the same floor, It is a vector of all 1s. The same-level / upward transfer rate for level 1. For higher-level same-level / upward transfer rates, To provide feedback on the rate of upward migration caused by customers, The rate of downward transfer due to negative customers. , All are stage numbers.
[0055] In addition, embodiments of this application may also employ an exponential distribution to simulate service time (i.e., call duration) and follow a first-come, first-served rule. Furthermore, the exponential distribution can be extended to a staged distribution to handle more general service times.
[0056] In constructing the matrix, this application's embodiments include not only negative customer arrival rates. It also includes the impatience rate related to queue length. And the probability of feedback after the service is completed. These added constraints enable the method to move from being theoretically general to being practically specific, thus truly reflecting the complexity of the target application scenario.
[0057] In step 103, the quasi-birth-death process is decomposed into RG and the performance indicators of the target queuing system are calculated. The performance indicators include the average queue length and the average customer dwell time.
[0058] In this embodiment of the application, the RG decomposition method is invoked to decompose and solve the pseudo-birth and death process constructed in step 102, and then the average queue length and average customer stay time of the target queuing system are calculated using the solution results.
[0059] The embodiments of this application accurately predict performance indicators such as average queue length and customer dwell time, helping call center managers understand the system's operational status under different conditions. For example, if it is predicted that the average queue length will be relatively long within a certain time period, managers can increase the number of service personnel or optimize service processes in advance to reduce customer waiting time and improve service quality. At the same time, based on the predicted customer dwell time, service resources can be rationally allocated to ensure that customers receive service within a reasonable time, thereby improving resource utilization efficiency.
[0060] In one possible implementation, when the quasi-birth-death process is the first quasi-birth-death process, and when the performance index is the average queue length, the quasi-birth-death process is decomposed into RG decomposition to calculate the performance index of the target queuing system, which may include: The first pseudo-birth-death process is decomposed into RG to obtain the first R measure; Calculate the stationary probability vector of the target queuing system using the first R measure; The average queue length of the target queuing system is calculated using a stationary probability vector.
[0061] Optionally, the RG decomposition method can be used to analyze the first pseudo-birth-death process. The R measure is obtained by decomposition and iterative calculation. The specific calculation process is as follows:
[0062]
[0063]
[0064]
[0065]
[0066] in, For the first R measure, For the first Layer, First The upward transition matrix of the stage. For the first Layer, First The downward transition matrix of the stage. , All are stage indexes. A basic index for customer quantity levels. For the first Layer, First The downward transition matrix of the stage. is a sub-block matrix in the generator matrix of the first pseudo-birth and death process.
[0067] By linearly solving the first R measure, i.e., by using the above formula to solve a system of linear equations, the stationary probability vector of the initial state can be obtained. The corresponding solution to the linear equation system is as follows:
[0068] And because of custom coefficients The stationary probability vector of the target queuing system is obtained. .
[0069] Then, based on the calculated stationary probability vector The average queue length of the target queuing system is calculated, i.e.:
[0070] in, This represents the average queue length.
[0071] In one possible implementation, when the quasi-birth-death process is a second quasi-birth-death process, and when the performance metric is the average customer dwell time, the quasi-birth-death process is decomposed into RGs to calculate the performance metrics of the target queuing system, which may include: The second pseudo-birth-death process is decomposed into RG measures to obtain the U measure, the second R measure, and the G measure; The first matrix is calculated using the U measure, the second R measure, and the G measure; The average customer dwell time is calculated based on the first matrix.
[0072] Optionally, solve for the inverse matrix of the second pseudo-birth-death process. .
[0073] remember ,in:
[0074]
[0075] in, , , , All are transfer rate blocks between non-absorption states submatrix, Submatrix The complement matrix.
[0076] The second pseudo-birth-death process is decomposed using the RG decomposition method, and the second matrix is calculated. .
[0077] The U-measure is defined as follows: .
[0078] Define the second R measure as: .
[0079] Define the G measure as: .
[0080] The second matrix can be obtained using the U measure, the second R measure, and the G measure. ,Right now:
[0081]
[0082]
[0083] make ;
[0084]
[0085]
[0086]
[0087] in, For the second R measure, For U measure, Let G be the measure. for The Layer, First Submatrix of columns, for The Layer, First Submatrices of columns.
[0088] Therefore there is Bring it in Then the first matrix can be calculated. .
[0089] Then, the first matrix obtained through calculation is used. The average customer dwell time is calculated as follows:
[0090] in, Indicates an absorption state The initial probability vector of the Markov process.
[0091] This application provides a method for predicting the performance of a call center queuing system. The method involves acquiring system parameters of the target queuing system, including stage distribution parameters, service rate, impatience rate, negative customer arrival rate, and feedback probability. Based on these parameters, a quasi-birth-death process is constructed. This process is then subjected to RG decomposition to calculate the performance indicators of the target queuing system, including average queue length and average customer dwell time. The method utilizes the acquired system parameters to construct the quasi-birth-death process, a powerful mathematical tool capable of accurately describing queuing systems with complex state transitions. By abstracting the actual queuing system into a quasi-birth-death process, the transition patterns between different states can be more accurately characterized, thereby improving the accuracy of performance indicator calculations. Furthermore, accurately predicting performance indicators such as average queue length and customer dwell time helps call center managers understand the system's operational status under different conditions. Simultaneously, based on the predicted customer dwell time, service resources can be rationally allocated to ensure customers receive service within a reasonable timeframe, improving resource utilization efficiency.
[0092] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.
[0093] The following are device embodiments of this application. For details not described in detail, please refer to the corresponding method embodiments described above.
[0094] Figure 4 A schematic diagram of the performance prediction device for a call center queuing system provided in an embodiment of this application is shown. For ease of explanation, only the parts related to the embodiment of this application are shown, and are described in detail below: like Figure 4 As shown, the call center queuing system performance prediction device 4 includes: The parameter acquisition module 41 is used to acquire the system parameters of the target queuing system. The system parameters include the stage distribution parameters, service rate, impatience rate, negative customer arrival rate, and feedback probability. Process construction module 42 is used to construct a pseudo-birth and death process based on the system parameters of the target queuing system; The performance calculation module 43 is used to perform RG decomposition on the quasi-birth-death process and calculate the performance indicators of the target queuing system, including the average queue length and the average customer dwell time.
[0095] This application provides a performance prediction device for a call center queuing system. It acquires system parameters of the target queuing system, including staged distribution parameters, service rate, impatience rate, negative customer arrival rate, and feedback probability. Based on these parameters, a quasi-birth-death process is constructed. The quasi-birth-death process is then decomposed using RG decomposition to calculate performance indicators of the target queuing system, including average queue length and average customer dwell time. This application constructs a quasi-birth-death process based on the acquired system parameters. Quasi-birth-death processes are powerful mathematical tools capable of accurately describing queuing systems with complex state transitions. By abstracting the actual queuing system into a quasi-birth-death process, the transition patterns between different states can be more accurately characterized, thereby improving the accuracy of system performance indicator calculations. Furthermore, accurately predicting performance indicators such as average queue length and customer dwell time helps call center managers understand the system's operating status under different conditions. Simultaneously, based on the predicted customer dwell time, service resources can be rationally allocated to ensure customers receive service within a reasonable timeframe, improving resource utilization efficiency.
[0096] In one possible implementation, the quasi-birth-death process includes a first quasi-birth-death process determined by the number of customers and the customer arrival process stage; the process building module can be used for: Based on the number of customers and the stages of the customer arrival process, construct the state transition relationship of a two-dimensional Markov process; The state space is determined based on the state transition relationship of a two-dimensional Markov process. Based on the state space, the first pseudo-birth and death process is obtained.
[0097] In one possible implementation, when the performance metric is the average queue length, the performance calculation module can be used to: The first pseudo-birth-death process is decomposed into RG to obtain the first R measure; Calculate the stationary probability vector of the target queuing system using the first R measure; The average queue length of the target queuing system is calculated using a stationary probability vector.
[0098] In one possible implementation, the performance calculation module can also be used for: By solving the first R measure linearly, the stationary probability vector of the target queuing system is obtained.
[0099] In one possible implementation, the quasi-birth-death process includes a second quasi-birth-death process determined by the number of customers when the target customer arrives, the number of customers after the target customer arrives, and the customer arrival process stage, where the target customer is a customer who arrives at any time in the target queuing system. The process building module can also be used for: Based on the number of customers when the target customer arrives, the number of customers after the target customer arrives, and the stage of the customer arrival process, a Markov process with an absorption state is constructed. Based on the Markov process with an absorbing state, a second pseudo-birth-death process is constructed.
[0100] In one possible implementation, when the performance metric is the average customer dwell time, the performance calculation module can also be used for: The second pseudo-birth-death process is decomposed into RG measures to obtain the U measure, the second R measure, and the G measure; The first matrix is calculated using the U measure, the second R measure, and the G measure; The average customer dwell time is calculated based on the first matrix.
[0101] In one possible implementation, the performance calculation module can also be used for: The second matrix is calculated based on the U measure, the second R measure, and the G measure; Calculate the inverse of the second matrix and use the inverse of the second matrix as the first matrix.
[0102] Figure 5 This is a schematic diagram of the terminal provided in an embodiment of this application. For example... Figure 5 As shown, the terminal 5 in this embodiment includes: a processor 50, a memory 51, and a computer program 52 stored in the memory 51 and executable on the processor 50. When the processor 50 executes the computer program 52, it implements the steps in the various call center queuing system performance prediction method embodiments described above, for example... Figure 1 Steps 101 to 103 are shown. Alternatively, when the processor 50 executes the computer program 52, it implements the functions of each module / unit in the above-described device embodiments, for example... Figure 4 The functions of each module are shown.
[0103] For example, the computer program 52 can be divided into one or more modules / units, which are stored in the memory 51 and executed by the processor 50 to complete this application. The one or more modules / units can be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program 52 in the terminal 5. For example, the computer program 52 can be divided into... Figure 4 The modules shown.
[0104] The terminal 5 can be a computing device such as a desktop computer, laptop, handheld computer, or cloud server. The terminal 5 may include, but is not limited to, a processor 50 and a memory 51. Those skilled in the art will understand that... Figure 5 This is merely an example of terminal 5 and does not constitute a limitation on terminal 5. It may include more or fewer components than shown, or combine certain components, or different components. For example, the terminal may also include input / output devices, network access devices, buses, etc.
[0105] The processor 50 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.
[0106] The memory 51 can be an internal storage unit of the terminal 5, such as a hard disk or memory of the terminal 5. The memory 51 can also be an external storage device of the terminal 5, such as a plug-in hard disk, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card equipped on the terminal 5. Furthermore, the memory 51 can include both internal storage units and external storage devices of the terminal 5. The memory 51 is used to store the computer program and other programs and data required by the terminal. The memory 51 can also be used to temporarily store data that has been output or will be output.
[0107] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.
[0108] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.
[0109] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.
[0110] In the embodiments provided in this application, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling or direct coupling or communication connection may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.
[0111] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.
[0112] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.
[0113] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above-described embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various call center queuing system performance prediction method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.
[0114] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.
Claims
1. A method for predicting the performance of a call center queuing system, characterized in that, include: Obtain the system parameters of the target queuing system, including stage distribution parameters, service rate, impatience rate, negative customer arrival rate, and feedback probability; Based on the system parameters of the target queuing system, a pseudo-birth-death process is constructed; The quasi-birth-death process is decomposed using RG decomposition to calculate the performance indicators of the target queuing system, including the average queue length and the average customer dwell time.
2. The call center queuing system performance prediction method according to claim 1, characterized in that, The simulated birth-and-death process includes a first simulated birth-and-death process determined by the number of customers and the customer arrival process stage; the construction of the simulated birth-and-death process based on the system parameters of the target queuing system includes: Based on the number of customers and the stage of the customer arrival process, construct the state transition relationship of a two-dimensional Markov process; The state space is determined based on the state transition relationship of the two-dimensional Markov process. Based on the state space, the first pseudo-birth and death process is obtained.
3. The call center queuing system performance prediction method according to claim 2, characterized in that, When the performance metric is the average queue length, the step of performing RG decomposition on the pseudo-birth-death process and calculating the performance metric of the target queuing system includes: The first pseudo-birth-death process is decomposed into RG to obtain the first R measure; Using the first R measure, calculate the stationary probability vector of the target queuing system; The average queue length of the target queuing system is calculated using the stationary probability vector.
4. The call center queuing system performance prediction method according to claim 3, characterized in that, The step of calculating the stationary probability vector of the target queuing system using the first R measure includes: The stationary probability vector of the target queuing system is obtained by linearly solving the first R measure.
5. The call center queuing system performance prediction method according to claim 1, characterized in that, The simulated birth and death process includes a second simulated birth and death process determined by the number of customers when the target customer arrives, the number of customers after the target customer arrives, and the customer arrival process stage, wherein the target customer is a customer who arrives at any time in the target queuing system; The process of constructing a pseudo-birth and death process based on the system parameters of the target queuing system includes: Based on the number of customers when the target customer arrives, the number of customers after the target customer arrives, and the stage of the customer arrival process, a Markov process with an absorption state is constructed. Based on the Markov process with the absorption state, the second pseudo-birth-death process is constructed.
6. The call center queuing system performance prediction method according to claim 5, characterized in that, When the performance metric is the average customer dwell time, the step of performing RG decomposition on the pseudo-birth-death process and calculating the performance metric of the target queuing system includes: The second pseudo-birth-death process is decomposed into RG measures to obtain the U measure, the second R measure, and the G measure; The first matrix is calculated using the U measure, the second R measure, and the G measure; The average stay time of the customer is calculated based on the first matrix.
7. The call center queuing system performance prediction method according to claim 6, characterized in that, The calculation of the first matrix using the U measure, the second R measure, and the G measure includes: The second matrix is calculated based on the U measure, the second R measure, and the G measure; Calculate the inverse of the second matrix, and use the inverse of the second matrix as the first matrix.
8. A performance prediction device for a call center queuing system, characterized in that, include: The parameter acquisition module is used to acquire the system parameters of the target queuing system, including the stage distribution parameters, service rate, impatience rate, negative customer arrival rate, and feedback probability. The process construction module is used to construct a pseudo-birth and death process based on the system parameters of the target queuing system; The performance calculation module is used to perform RG decomposition on the quasi-birth-death process and calculate the performance indicators of the target queuing system, including the average queue length and the average customer stay time.
9. A terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the call center queuing system performance prediction method as described in any one of claims 1 to 7.
10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the call center queuing system performance prediction method as described in any one of claims 1 to 7.